To solve the system of equations:
- \( x - 5y = 16 \) (Equation 1)
- \( -4x - 8y = -8 \) (Equation 2)
First, we'll simplify Equation 2. We can divide the entire equation by -4:
\[ \frac{-4x}{-4} + \frac{-8y}{-4} = \frac{-8}{-4} \] This simplifies to:
\[ x + 2y = 2 \quad (Equation \ 3) \]
Now we have two equations:
- \( x - 5y = 16 \) (Equation 1)
- \( x + 2y = 2 \) (Equation 3)
Next, we can solve for \( x \) from Equation 3:
\[ x = 2 - 2y \quad (Equation \ 4) \]
Now, we'll substitute Equation 4 into Equation 1:
\[ (2 - 2y) - 5y = 16 \]
Combine like terms:
\[ 2 - 7y = 16 \]
Now, isolate \( y \):
\[ -7y = 16 - 2 \] \[ -7y = 14 \] \[ y = -2 \]
Now that we have \( y \), we can substitute it back into Equation 4 to find \( x \):
\[ x = 2 - 2(-2) \] \[ x = 2 + 4 \] \[ x = 6 \]
So, the solution to the system of equations is:
\[ x = 6, \quad y = -2 \]
The solution can be written as the ordered pair \((6, -2)\).